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The third helpful notion is that it is not enough to think problems through forward. You must also think in reverse, much like the rustic who wanted to know where he was going to die so that he’d never go there. Indeed, many problems can’t be solved forward. And that is why the great algebraist Carl Jacobi so often said, “Invert, always invert,” and
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The third helpful notion is that it is not enough to think problems through forward. You must also think in reverse, much like the rustic who wanted to know where he was going to die so that he’d never go there. Indeed, many problems can’t be solved forward. And that is why the great algebraist Carl Jacobi so often said, “Invert, always invert,” and why the Pythagoreans51 thought in reverse to prove that the square root of two was an irrational number.
applied inversion. Here is a brief explanation of his process: Identify the problem Define your objective Identify the forces that support change towards your objective Identify the forces that impede change towards the objective Strategize a solution! This may involve both augmenting or adding to the forces in step 3, and reducing or eliminating the forces in step 4.
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Most people, if you describe a train of events to them will tell you what the result would be. They can put those events together in their minds, and argue from them that something will come to pass. There are few people, however, who, if you told them a result, would be able to evolve from their own inner consciousness what the steps were which led up to that result. This power is what I mean when I talk of reasoning backward, or analytically.
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